Eigenvalue decomposition is used in a very wide range of fields such as chemical calculation using molecular orbital method, statistical calculation, information search, and the like. Also, methods of eigenvalue decomposition are known (see Non-Patent Document 1, for example).
[Non-Patent Document 1] J. J. M. Cuppen, “A divide and conquer method for the symmetric tridiagonal eigenproblem”, Numerische Mathematik, Vol. 36, pp. 177-195, 1981